A method of the kind mentioned in the opening paragraph and a device for carrying out said method are known from German Patent A1 3546216. In this known method, an electronic component (chip) is transported to a feed position by a supply device. In this feed position, a manipulator controlled by a control system picks up the component by means of an underpressure and moves it into an image field of an imaging device. A picture of the component is then taken by means of the imaging device. In an image signal processor, this picture is compared with a model picture of the component stored in this processor, and deviations in an x- and a y-direction and an angular deviation about a z-axis are computed. An x-axis and a y-axis, which define the x- and y-directions, lie in a plane parallel to the printed circuit board on which the component is to be placed. The z-axis is directed transversely to this plane and coincides with an axis of rotation of the manipulator. After the deviations have been computed, the component is rotated through an angle by the manipulator and is put in the desired position on the printed circuit board, during which the computed deviations are taken into account. During imaging of the component it is necessary for the manipulator to be in a position relative to the imaging device which is known beforehand. The position of the manipulator is determined by the control system. If the manipulator moves at a certain speed relative to the imaging device during imaging, the exact position of the manipulator at the imaging moment cannot be accurately determined by means of the control system. A disadvantage of this method and of this device is that, if the manipulator position relative to the imaging device deviates from the expected position, the position of the component relative to the imaging device cannot be well determined, and faulty corrections will be carried out. For example, if the component is picked up eccentrically by the manipulator, a rotation about the z-axis will cause deviations in the x- and y-directions. If the position of the manipulator relative to the imaging device is known, these deviations can be corrected during placement on the printed circuit board. If this position is not accurately known, these deviations cannot be corrected.